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Students in this video, let's discuss perpendicular lines now, let's have two lines and let them one

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and aim to be the slopes of these two lines.

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All right.

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Now, if these two lines are perpendicular, that is if they are intersecting at an angle, forming

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90 degree.

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Right.

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Then M1 and M2 will have this relation that is M1 into M2 will be equal to minus one.

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Now, why is that so we know that the angle between two lines is given by Dante is equal to more of

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in one minus M2, two by one plus M1, M2 right now, when M1 into M2 is equal to minus one over here

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you can see that the denominator becomes zero.

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Right.

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And division by zero is not defined.

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So when M1 into M2 is equal to minus one, Dante De is equal to infinity or it is not defined.

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Now, in technology, you will have learned that Danto is infinity when data is equal to 90 degrees.

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That's why when two given lines with Slope's M1 and M2 are perpendicular, then M1 into M2 will be equal

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to minus one.

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All right, let's take two lines where this is true.

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Let's have a X plus by plus one is equal to zero and B minus Ebeye.

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Let's see, two is equal to zero.

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All right.

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Now why did I constructed like this?

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You can see that I have a B over here and it has been interchanged and over here you have a plus sign

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and this has become minus.

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Let's try to see why that is so.

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All right.

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Let me make some space over here.

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What is the slope of the first line over here?

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You can see that the slope over here, M1 is minus eight by B, right.

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Or do you find that you have to write it in the form Y is equal to an explicit.

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So you will get that Y is equal to minus eight by B, X plus something right up the slope over here

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is minus Abib.

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What about the slope over here you will see that the slope over here is equal to be by eight.

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And when you multiply these two together you can see that you will get minus one.

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Right, minus B into B, it gives you minus one.

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Therefore there is this an interesting property.

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If you are given one line and if you want to write the line, which is perpendicular to this line,

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you just need to change the coefficients and change the sign over here.

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That is, let me make some space over here.

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If you have given X plus by places equal to zero and you want to write a line that is perpendicular

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to this line, that line would have the coefficient that's over here for white for X.

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That is because and the coefficient for it will be given to be that is a right.

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But all you need to change the sine so this will become minus a white plus int. equals zero.

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So this line will be perpendicular to this line.

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And we have seen the reason over here.

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Over here the slope is minus Ebi B and over here the slope is B by and if you multiply them you get

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minus one.

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And that makes tanty the equal to infinity and hence the it is equal to 90 degrees.